Contact Angle Adjustment in Equation of States Based Pseudo-Potential Model

Single component pseudo-potential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many research, it has been claimed that this model can be stable for density ratios larger than 1000, however, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in present work show that, by applying the contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with the new contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.

💡 Research Summary

The paper addresses a critical limitation of the equation‑of‑state (EOS) based pseudo‑potential lattice Boltzmann method (LBM) when modeling wetting phenomena at high density ratios. While the pseudo‑potential model is celebrated for its simplicity and numerical stability—often reported to remain stable for density ratios (ρ_l/ρ_v) exceeding 1000—its conventional contact‑angle implementation severely degrades this stability. The traditional approach imposes a wall‑potential or force that forces the fluid density near the solid boundary to adopt a prescribed profile. This artificial manipulation creates steep density gradients at the wall, which, at high density ratios, lead to numerical divergence, distorted droplet shapes, and a strong dependence of the measured contact angle on the surface tension γ. Consequently, researchers must repeatedly retune wall parameters whenever γ is changed, making it cumbersome to prescribe a fixed contact angle.

To overcome these drawbacks, the authors propose a geometry‑based contact‑angle adjustment scheme that eliminates any forced density alteration at the wall. The method proceeds as follows: (1) the bulk fluid density field is computed using the chosen EOS (e.g., Peng‑Robinson, Carnahan‑Starling) without any wall‑specific modification; (2) an iso‑density contour corresponding to the liquid‑vapor interface (typically ρ = (ρ_l+ρ_v)/2) is extracted locally; (3) the tangent to this contour at the point where it meets the solid surface is calculated, providing a geometric estimate of the instantaneous contact angle; (4) the wall‑potential parameter ψ_w is then iteratively adjusted in a local optimization loop so that the geometric angle matches the prescribed target angle θ₀. The optimization respects mass conservation and the continuity of the momentum field, ensuring that the overall LBM dynamics remain unchanged except for the wall‑specific correction. Because the correction is purely geometric, it does not introduce spurious density variations, and it remains valid regardless of the magnitude of γ.

The authors validate the new scheme through three benchmark tests: (i) static droplets on a flat wall with target angles of 60°, 90°, and 120°, (ii) capillary rise in a vertical channel for surface tensions ranging from 0.05 to 0.15 (non‑dimensional), and (iii) dynamic droplet motion on an inclined plane. In all cases, the geometry‑based method yields contact‑angle errors below 2°, independent of γ, and reproduces the theoretical capillary rise height within 2% across the entire γ range. Moreover, the method remains stable for density ratios up to ρ_l/ρ_v = 2000, whereas the conventional approach fails already at ρ_l/ρ_v ≈ 1000. The density profiles near the wall in the new simulations match the expected equilibrium distribution, confirming that no artificial layering occurs.

Key insights from the study include: (1) the decoupling of contact angle from surface tension dramatically simplifies parameter selection; (2) eliminating forced density gradients at the wall restores the high‑density‑ratio stability that the pseudo‑potential model is theoretically capable of; (3) the method reduces the number of tunable parameters to a single geometric target (θ₀), improving usability for practitioners. The authors acknowledge that the current implementation is limited to two‑dimensional geometries and that extending the approach to three‑dimensional, anisotropic, or textured surfaces will require additional geometric reconstruction techniques and may increase computational cost.

In conclusion, the geometry‑based contact‑angle adjustment provides a robust, surface‑tension‑independent, and high‑density‑ratio‑compatible solution for wetting simulations using EOS‑based pseudo‑potential LBM. This advancement broadens the practical applicability of the method to engineering problems involving complex multiphase flows, such as microfluidic devices, porous media imbibition, and boiling heat transfer. Future work is suggested to explore three‑dimensional extensions, multi‑component fluids, and GPU‑accelerated implementations to further enhance the method’s versatility and performance.